I am reading the book "Gravitaion and Cosmology" by S. Weinberg. In section 10.9, while discussing Lie derivatives of tensors of different ranks, he makes a general comment:
The effect of an infinitesimal coordinate transformation on any tensor $T$ is that the new tensor equals the old tensor at the same coordinate point, plus the Lie derivative of the tensor.
Is there a straightforward way to see this?
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